the only concern about pumping the lever with the bleeder open is that you are running the master cylinder piston across a part of the master cylinder that it normally doesn’t reach. On older brakes, rubbish can collect in there and damage the seals.
In systems where you can top up the reservoir or fit a funnel, gravity bleeding is a good idea to start with – just open the bleeder at the caliper and let fluid flow down through the system, keep topping up the reservoir, obviously. If that doesn’t work, then try gently pumping the lever to force fluid through the system.
Fit old pads when you bleed. This will let the caliper pistons extend a little, so the system will be overfilled. Then, when you are finished, leave the bleed port on the master cylinder open and use a screwdriver to lever the pads apart and push the pistons back into the caliper. This will force the excess fluid out of the master cylinder reservoir and make sure it is completely full, without any air bubbles. Then fit your good pads. (However, it’s a good idea to clean the pistons first with a toothbrush or something and warm soapy water, then rinse them off with hot water, then lube them with a few drops of brake fluid. This stop dirt and rubbish getting force into the piston seals when you push the pistons back in.)